Respuesta :
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex](a-2)(a+1)+(a-2)(a+4)[/tex]STEP 2: Separate the expression into 2 parts
[tex]\begin{gathered} (a-2)(a+1)---A \\ (a-2)(a+4)----B \\ \text{Expression}=A+B \end{gathered}[/tex]STEP 3: Factorize Part A
[tex]A=(a-2)\times(a+1)[/tex]STEP 4: Factorize Part B
[tex]B=(a-2)\times(a+4)[/tex]STEP 5: Write out the common factor
[tex]\begin{gathered} \text{Common factor is the factor that can }be\text{ se}en\text{ in both parts of the expression} \\ \text{Common Factor}\Rightarrow(a-2) \\ \\ \text{Factoring out the co}mmon\text{ factor, we have the expression as;} \\ (a-2)\lbrack(a+1)+(a+4)\rbrack \\ \Rightarrow(a-2)\lbrack a+1+a+4\rbrack \\ \Rightarrow(a-2)(2a+5) \end{gathered}[/tex]Hence, the correct choice is A and the answer in factored form is:
[tex](a-2)(2a+5)[/tex]